The Davydov or exciton splitting of vertical excitation energies is commonly used to estimate the excitation energy transfer rate between chromophores. Here we investigate the S1-S2 Davydov splitting in 2-pyridone dimer as a function of the monomer separation, R. We assess the ability of various functionals to reproduce the Davydov splitting at finite R predicted by the approximate coupled cluster singles doubles method CC2. While semilocal functionals fail qualitatively because of spurious charge-transfer intruder states, global hybrids with a large fraction of exact exchange, such as BHandH-LYP, reproduce the CC2 splittings within few wavenumbers. We analyze our results by comparison to lowest-order intermolecular perturbation theory in the spirit of Förster and Dexter. At equilibrium hydrogen bond distance, the Förster-Dexter splittings are too small by up to a factor of 2.